I want to buy an iPhone 8. However, in a few days new iPhone 11 will be released. Can I expect older models to become cheaper at that moment or soon afterwards? Or does the price drop happen before the release?

Since shopping questions aren’t encouraged here - the scope of this is official Apple list price - historical behaviors, and not speculation about some future Apple release cycle even if one is imminent.

Historically, Apple announces new models and pricing and at the same time, refreshes their official pricing the same day as the keynote / press release. Additionally, look online and at Apple stores as they then sell (often at further discount) any now “discontinued” models in the Certified Refurbished / Clearance section:

Apple typically announces new phone models in September. The new phone models usually take the spot at the high end of Apple’s pricing structure and the last one or two years of models slide down in price to become the “low cost” iPhone options. The pricing change occurs right as the new iPhones are announced, even if the new phones won’t ship for another month or two.

Here in 2019, Apple just announced its new phone lineup last week. iPhone 8 now sits at the bottom of the pricing structure. The price adjustments have already been made for this phone release cycle.